Mixture and Alligation Problems Tricks and Shortcuts With Examples

We usually see questions based on Mixtures and alligations in which two types of elements having cheaper and dearer costs are mixed together. In which you require to find the mean cost, the ratio of quantities in which they should be mixed in and much more.

Note:

• Always put cheaper price item at left and dearer(expensive) price item at the right
• Mixed price would never less or more than cheaper and dearer item
• Ratio always be in form of = (Type 2 price – Mixed price)/(Mixed price – Type 1 price)

Types of Question With Mixture and Alligation tricks

• Find Quantity or Ratio

  • Simply use the formula

Q. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

Cheaper quantity/ Dearer quantity = 3.5/1.5

= 7/3 = 7:3

• When the mixed price or value is missing

  • Add to cheaper value with the dearer quantity or Subtract a dearer value from the cheaper quantity

Q. The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

Step 1 .  15 + 3 = 18   0r 20 -2 = 18

Answer Rs 18 per kg

• When three items are mixed

  • Create possible pairs in  such a way that mixed values lie in between the value of the given items, usually have 2 groups
  • Apply allegation rule on possible pairs
  • The item which is similar in both combinations its quantity value must be added together

Q. Tea worth Rs. 126 per kg, Rs. 135 per kg and Rs 175.5 per kg are mixed together. If the mixture is worth Rs. 153 per kg, then the ratio in which they mixed:

Step 1.  Item   A = 126   B  =135       C =175.5

Possible pairs where mean value can 153 lie

(A and C), and (B and C)

Now Apply rule on these combinations

Step 2:  A’s quantity = 22.5, B’s quantity = 22.5  and C is the same in group 1 and group 2, its quantity should be added  ( 27 +18)

= Ratio  = 22.5 : 22.5 :45

= 1: 1: 2

• When item’s compositions are given in ratio, for example, Milk =  milk : water,

  • Choose any one of the associated ingredients
  • Apply alligation rule

Q. Two vessels A and B contain spirit and water mixed in the ratio 5: 2 and 7: 6 respectively. Find the ratio in which this mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8: 5?

Step 1. A = 5:2 B = 7:6  C = 8:5

Choosing water as one of the ingrediant , so now

A = 2/7 , B = 6/13   C = 5/13

Step 2. Applying rule,

1/13 : 9/91

cross muliplication,

=91:117

=7:9